There is no direct way to calculate the minimum and maximum from the Raster Calculator in QGIS. The only workaround is to extract the minimum and maximum of the raster layer using Raster layer statistics
tool from Processing Toolbox, and save it into a text editor:
Then use the above minimum and maximum values in the raster calculator from Processing Toolbox NOT from Raster toolbar main menu.
Here is an example:
This is the input raster:

Using Raster Calculator from Processing Toolbox:

The output will be like this:

As you can see the range is not set to minimum 0 to maximum 1 because the QGIS is not rendering statistics correctly. You need to re-render it from Layer Properties -> Symbology -> Statistics

Click Apply
and it will be updated to 0 and 1 range:
